The Fifty-Nine Icosahedra

He carried out the original analysis based on Miller's rules, adopting a number of techniques such as combinatorics and abstract graph theory whose use in a geometrical context was then novel.

[2] John Flinders Petrie was a lifelong friend of Coxeter and had a remarkable ability to visualise four-dimensional geometry.

His direct contribution to the fifty nine icosahedra was the exquisite set of three-dimensional drawings which provide much of the fascination of the published work.

They also added a reference section containing tables, diagrams, and photographs of some of the Cambridge models (which at that time were all thought to be Flather's).

Since publication of The 59, Wenninger published instructions on making models of some; the numbering scheme used in his book has become widely referenced, although he only recorded a few stellations.

The stellation diagram for the icosahedron with the central triangle marked for the original icosahedron
Stellation diagram with numbered face sets
Cell diagram with Du Val notation for cells